formulas, I always advise checking with loading manuals. VI. ConClusIons
is best represented by Powley’s r0.375 Miller’s r0.4
Our Figures and Tables show how well these various approximations fit the quite scattered data. Overall, (c2
formula; next best by /c1 ; then the iterated values; and finally by Barsness’
formula, which is increasingly poor as r grows very large or very small. All but Barsness’ formula have a theoretical basis. I recommend Powley’s 3/8 rule because it is both the best
and easiest to use with a hand calculator. With a yx key use (c2
/c1) = (m1/m2)0.375
Alternatively multiply r= by itself three times and take the square root three times, i.e.
c2 /c1 = r x r x r Finally I offer my slogan for safety: A clever reloader,
defined as one who is still alive and intact, is a chicken reloader. Remember the qualifications: ALWAYS check re- loading manuals.
Donald G. Miller 2862 Waverly Way Livermore, CA 94551
don.miller9@
comcast.net
I thank my daughter Nancy Miller and friends Mic
McPherson and By Smalley for improving this article's clar- ity, and McPherson and Smalley for greatly improving its accuracy as well. Any mistakes are mine.
References [B10] John Barsness, “Some Simple Ballistic Math,”
The Varmint Hunter Magazine, January-March (Issue #73), 74-76 (2010). [Ch08] Prosper Charbonnier, “Balistique Intérieure,” O. Doin, Paris, 1908. pp 323-324. [Cl28] C. A. Clemmow, “A Theory of Interior Ballistics
Based on a Pressure Index Law of Burning for Propellants,” Phil. Trans. Royal Soc. (London) 227A, 345-382 (1928). [Co50] J. Corner, “Theory of the Interior Ballistics of Guns,” John Wiley, New York, 1950. pp 207-209. [D86] W. C. Davis, Jr., Ed., “Handloading,” NRA, 2nd printing, 1986, pp 133-137. [GL05] Fernand Gossot and Roger Liouville, “Sur les
effets balistiques des poudres sans fumée dans les bouches à feu,” Mémorial de l’Artillerie de la Marine XXXIII (1905). Also Mémorial des Poudres, XIII (1905-1906). [I96] “Handloader's Guide for Smokeless Powders,” IMR Powder Co., Plattsburgh, N.Y. 1996 edition. [McP96] M. L. McPherson, “The Handloader's Di-
lemma,” in The 1996 Precision Shooting Annual, Precision Shooting, Manchester, CT, pp 288-313. [McP10] M. L. McPherson, email, August, 2010. [M08] Don Miller (Donald G. Miller), “The ‘Barsness
4-to-1 Rule’: The Effect of Increased Case Capacity on Veloc- ity,” The Varmint Hunter Magazine, April-June (Issue #66), 178-181 (2008). [M10] Don Miller (Donald G. Miller), “The ‘Barsness
v-m Rule’” The Varmint Hunter Magazine, October-Decem- ber (Issue #76), xxx (2010). [P79] Homer Powley, Technical Memorandum no. 148,
)
“Ratio of Peak Pressure to Mean Pressure,” December, 1979. In this hard-to-find reference, Powley‘s actual equation is equivalent to the difference approximation to the logarithmic derivative of. It doesn’t work for very large or very small r values.
[W55] M. D. Waite, “Bullet Types and Pressures,” American Rifleman, June, 52 (1955).
—Table 1A High m1 to Low m2 30-06 only—
Variable Mean StDev Min. Max. Range B c2 res
2.64
M 0.4 c2 res 0.15 0.39 7.11
B c2 %res M 0.4 c2 %res 0.55
2.66 -1.65 1.26 -2.71
P 0.375 c2 res -0.23 1.30 -2.92 iter c2 res
1.27 -2.59
P 0.375 c2 %res -0.44 3.19 -6.78 iter c2 %res 1.32
3.38 -5.94
8.50 10.15 1.71 4.42 1.47 4.39 2.02 4.61
6.73 -3.79 20.37 24.16 3.13 -6.23
5.44 11.67 4.33 11.11 7.49 13.43
— Table 1B Low m1 to High m2 30-06 only —
Variable Mean StDev Min. Max. Range B c2 res
M 0.4 c2 res -0.13 1.13 -1.59 P 0.375 c2 res 0.19 iter c2 res
B c2 %res
M 0.4 c2 %res -0.48 2.46 -4.20 P 0.375 c2 %res 0.22
iter c2 %res -1.07 2.66 -5.78
-0.34 1.15 -1.74 -1.82 2.52 -5.91 2.48 -3.38
-0.70 1.13 -2.27 1.16 -1.37
1.88 4.15 2.52 4.10 2.73 4.10 2.43 4.16
3.79 9.70 5.09 9.29 5.51 8.89 4.91 10.69
— Table 2A High m1 to Low m2 196 points —
Variable Mean StDev Min. Median Max. B c2 res
2.12
M 0.4 c2 res 0.69 P 0.375 c2 res 0.43 iter c2 res
B c2 %res iter c2 %res
0.75 4.87
M 0.4 c2 %res 1.52 P 0.375 c2 %res 0.92 1.78
2.08 -2.42 1.46 -3.38 1.44 -3.58 1.46 -3.34
4.73 -6.03 3.43 -7.59 3.39 -8.08 3.52 -7.49
1.80 8.50 0.70 4.38 0.50 3.98 0.77 4.87
4.59 20.37 1.62 12.33 1.11 11.22 1.94 13.71
— Table 2B Low m1 to High m2 196 points —
Variable Mean StDev Min. Max. Range B c2 res
-1.22 1.41 -4.71
M 0.4 c2 res -0.62 1.34 -3.76 P 0.375 c2 res -0.39 1.319 -3.45 iter c2 res
-0.68 1.35 -4.21 B c2 %res
2.54 7.25 3.18 6.94 3.38 6.83 3.18 7.39
M 0.4 c2 %res -1.36 2.92 -10.15 6.38 16.53 P 0.375 c2 %res -0.87 2.90 -9.32
-2.63 2.98 -11.86 5.38 17.24 6.68 16.01
iter c2 %res -1.58 3.02 -11.38 6.13 17.52
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